we restored the scripts of \lambda\delta version 1

[helm.git] / helm / coq-contribs / LAMBDA-TYPES / pr0_subst0.v

diff --git a/helm/coq-contribs/LAMBDA-TYPES/pr0_subst0.v b/helm/coq-contribs/LAMBDA-TYPES/pr0_subst0.v
deleted file mode 100644 (file)
index 46a137e..0000000
--- a/helm/coq-contribs/LAMBDA-TYPES/pr0_subst0.v
+++ /dev/null
@@ -1,105 +0,0 @@
-Require subst0_gen.
-Require subst0_lift.
-Require subst0_subst0.
-Require subst0_confluence.
-Require pr0_defs.
-Require pr0_lift.
-
-(*#* #stop file *)
-
-   Section pr0_subst0. (*****************************************************)
-
-      Tactic Definition IH :=
-         Match Context With
-            | [ H1: (u1:?) (pr0 u1 ?1) -> ?; H2: (pr0 ?2 ?1) |- ? ] ->
-               LApply (H1 ?2); [ Clear H1; Intros H1 | XAuto ];
-               XElim H1; Intros
-            | [ H1: (u1:?) (pr0 ?1 u1) -> ?; H2: (pr0 ?1 ?2) |- ? ] ->
-               LApply (H1 ?2); [ Clear H1; Intros H1 | XAuto ];
-               XElim H1; Intros
-            | [ H1: (v1,w1:?; i:?) (subst0 i v1 ?1 w1) -> (v2:T) (pr0 v1 v2) -> ?;
-                H2: (subst0 ?2 ?3 ?1 ?4); H3: (pr0 ?3 ?5) |- ? ] ->
-               LApply (H1 ?3 ?4 ?2); [ Clear H1; Intros H1 | XAuto ];
-               LApply (H1 ?5); [ Clear H1; Intros H1 | XAuto ];
-               XElim H1; [ Intros | Intros H1; XElim H1; Intros ].
-
-      Theorem pr0_subst0_back: (u2,t1,t2:?; i:?) (subst0 i u2 t1 t2) ->
-                               (u1:?) (pr0 u1 u2) ->
-                               (EX t | (subst0 i u1 t1 t) & (pr0 t t2)).
-      Intros until 1; XElim H; Intros;
-      Repeat IH; XEAuto.
-      Qed.
-
-      Theorem pr0_subst0_fwd: (u2,t1,t2:?; i:?) (subst0 i u2 t1 t2) ->
-                              (u1:?) (pr0 u2 u1) ->
-                              (EX t | (subst0 i u1 t1 t) & (pr0 t2 t)).
-      Intros until 1; XElim H; Intros;
-      Repeat IH; XEAuto.
-      Qed.
-
-      Hints Resolve pr0_subst0_fwd : ltlc.
-
-(*#* #start file *)
-
-(*#* #caption "confluence with strict substitution" *)
-(*#* #cap #cap t1, t2 #alpha v1 in W1, v2 in W2, w1 in U1, w2 in U2 *)
-
-      Theorem pr0_subst0: (t1,t2:?) (pr0 t1 t2) ->
-                          (v1,w1:?; i:?) (subst0 i v1 t1 w1) ->
-                          (v2:?) (pr0 v1 v2) ->
-                          (pr0 w1 t2) \/
-                          (EX w2 | (pr0 w1 w2) & (subst0 i v2 t2 w2)).
-
-(*#* #stop file *)
-
-      Intros until 1; XElim H; Clear t1 t2; Intros.
-(* case 1: pr0_refl *)
-      XEAuto.
-(* case 2: pr0_cong *)
-      Subst0Gen; Rewrite H3; Repeat IH; XEAuto.
-(* case 3: pr0_beta *)
-      Repeat Subst0Gen; Rewrite H3; Try Rewrite H5; Try Rewrite H6;
-      Repeat IH; XEAuto.
-(* case 4: pr0_upsilon *)
-      Repeat Subst0Gen; Rewrite H6; Try Rewrite H8; Try Rewrite H9;
-      Repeat IH; XDEAuto 7.
-(* case 5: pr0_delta *)
-      Subst0Gen; Rewrite H4; Repeat IH;
-      [ XEAuto | Idtac | XEAuto | Idtac | XEAuto | Idtac | Idtac | Idtac ].
-      Subst0Subst0; Arith9'In H9 i; XEAuto.
-      Subst0Confluence; XEAuto.
-      Subst0Subst0; Arith9'In H10 i; XEAuto.
-      Subst0Confluence; XEAuto.
-      Subst0Subst0; Arith9'In H11 i; Subst0Confluence; XDEAuto 6.
-(* case 6: pr0_zeta *)
-      Repeat Subst0Gen; Rewrite H2; Try Rewrite H4; Try Rewrite H5;
-      Try (Simpl in H5; Rewrite <- minus_n_O in H5);
-      Try (Simpl in H6; Rewrite <- minus_n_O in H6);
-      Try IH; XEAuto.
-(* case 7: pr0_epsilon *)
-      Subst0Gen; Rewrite H1; Try IH; XEAuto.
-      Qed.
-
-   End pr0_subst0.
-
-      Tactic Definition Pr0Subst0 :=
-         Match Context With
-            | [ H1: (pr0 ?1 ?2); H2: (subst0 ?3 ?4 ?1 ?5);
-                H3: (pr0 ?4 ?6) |- ? ] ->
-               LApply (pr0_subst0 ?1 ?2); [ Clear H1; Intros H1 | XAuto ];
-               LApply (H1 ?4 ?5 ?3); [ Clear H1 H2; Intros H1 | XAuto ];
-               LApply (H1 ?6); [ Clear H1; Intros H1 | XAuto ];
-               XElim H1; [ Intros | Intros H1; XElim H1; Intros ]
-            | [ H1: (pr0 ?1 ?2); H2: (subst0 ?3 ?4 ?1 ?5) |- ? ] ->
-               LApply (pr0_subst0 ?1 ?2); [ Clear H1; Intros H1 | XAuto ];
-               LApply (H1 ?4 ?5 ?3); [ Clear H1 H2; Intros H1 | XAuto ];
-               LApply (H1 ?4); [ Clear H1; Intros H1 | XAuto ];
-               XElim H1; [ Intros | Intros H1; XElim H1; Intros ]
-            | [ _: (subst0 ?0 ?1 ?2 ?3); _: (pr0 ?4 ?1) |- ? ] ->
-               LApply (pr0_subst0_back ?1 ?2 ?3 ?0); [ Intros H_x | XAuto ];
-               LApply (H_x ?4); [ Clear H_x; Intros H_x | XAuto ];
-               XElim H_x; Intros
-            | [ H1: (subst0 ?0 ?1 ?2 ?3); H2: (pr0 ?1 ?4) |- ? ] ->
-               LApply (pr0_subst0_fwd ?1 ?2 ?3 ?0); [ Clear H1; Intros H1 | XAuto ];
-               LApply (H1 ?4); [ Clear H1 H2; Intros H1 | XAuto ];
-               XElim H1; Intros.